Zero faces problem with model for 3d print
As a noob myself I have noticed a big amount of zero faces. Selecting them by clicking the Zero Faces "text" in the 3d print result block make them show up in the model. They are small faces. I measured a really big one to be 4 millimeter by 10 millimeter. The rest of my faces (the models!) are about 70 by 20 millimeter. I assume therefore that they are small faces that clogg upp the model, and wont contribute much. One way I have figured out to fix them is to select the mesh and use Merge by distance. Merge by distance is found if you have added the Mesh tools addon. Look elsewhere for how to do that. Under Utility tools there I found the Merge by distance. Mesh tools appear in the Edit vertical menu under the 3dprint vertical menu. I selected a side of my model and entered Merge by distance as 0.02 meters ie 20 millimeters. (In the small popup down left in the big part of the screen.) I set the selection tool to faces before that, ofc. :) With this method I will go around the model and merge the small faces. 

So go around your model and select it and merge these small things away. Perhaps you can select the whole mesh and do it in one go. Good luck. 

Edit.Btw I guess that: - "Intersecting faces" are two faces where one go through another without an edge. "Thin Faces" are faces that are at least partially on top of each other. 

Edit 2: A more economical way of doing the same thing is selecting the "Thin Faces" in the 3d print addon, and then doing Select more in the Select (2nd row horisontal menu). This select adjacent faces as well as the original selection. Merging by distance will then correct that too. The merging by distance command works immediately so just shorten the distance gradually until your problem is solved.